Portfolio Systematic Risk

CFA Level I
#1

Apparently this answer is wrong:

As an investor increases the number of stocks in a portfolio, the systematic risk will remain constant.

I thought systematic risk cannot be diversitfied away because it is the risk that affects the entire stock market?

Can someone explain to me why this is the wrong answer?

#2

Yes, Systematic Risk cannot be avoided by the inclusion of more stocks, since it is inherent in the overall market.

However, Systematic risk can be magnified through selection or by using leverage, or diminished by including securities that have a low correlation with the portfolio, assuming they are not already part of the portfolio.

Therefore, while it cannot be eliminated, there is no reason that it must remain constant as the number of stocks in a portfolio increase.

Moreover, the only risk relevant in determining expected returns is Systematic Risk (as represented by the beta in CAPM). Why? Becasue in theory, rational investors are expected to completely diversify away the idiosyncratic risk/diversifiable risk.

#3

Maybe what I do not get is why beta represents systematic risk. If the market has its own risk (beta = 1), and a company has a beta of 1.5, how do you explain the 1.5 number in the context of a portfolio?

#4

The beta represents an asset’s sensitivity to market risk (aka systematic risk, non-diversifiable risk)

So if the the “market portfolio” were to increase (decrease) in value by 1%, an asset with beta 1.5 suggests that the asset value would increase (decrease) by 1.5%.

The same 1% increase in the market portfolio, will have different impacts on the other assets in the portfolio as determined by their corresponding betas.

To understand the portfolio effect you would calculate the portfolio beta - the individual asset betas are used to compute a weighted mean with weights being the proportion of each asset in the total portfolio value.

The sections in portfolio management will cover these concepts with plenty of examples.

#5

With all due respect, that is not at all what a beta of 1.5 means.

I wrote an article on beta that discusses, amongst other things, the common misunderstandings about beta: http://financialexamhelp123.com/beta/

What a beta of 1.5 means is that if the market _ return _ changes by 1%, the asset’s _ return _ will change, on average, 1.5%. But it’s possible that:

  • The market return changes from 4% to 5%, and the asset’s return changes from −10% to −8.5%
  • The market return changes from 4% to 5%, and the asset’s return changes from 10% to 11.5%
#6

Absolutely spot on. Apologies, I was very wrong indeed there.

Thanks Magician. Superb article as well !

#7

You’re too kind.

#8

So, basically, beta for a portfolio cannot become zero (eliminated) but you can change it from 1.5 to 2 or back down to 1 with the inclusion of certain securities in the portfolio?

#9

keep-running:

A beta from a protfolio could theoretically become zero. The portfolio beta is simply a (market) weighted average of the individual stocks’ betas. To get to a negative beta,

  1. Include negative beta securityto offset the positive beta securities in the portfolio (note: this is difficult to do other than by using derivatives)
  2. Take short positions in positive beta securities. Since a short position is effectively a negative weight, the contribution to portfolio beta of a short position is the same as a long position in a negative beta security.
#10

Ok, so beta of zero does not mean the portfolio is absent of beta?